Average Error: 58.1 → 57.1
Time: 23.7s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[\frac{0.5}{\frac{y}{x}} - \left(x \cdot x\right) \cdot 2\]
\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}
↓
\frac{0.5}{\frac{y}{x}} - \left(x \cdot x\right) \cdot 2
double f(double x, double y) {
        double r1134525 = 333.75;
        double r1134526 = y;
        double r1134527 = 6.0;
        double r1134528 = pow(r1134526, r1134527);
        double r1134529 = r1134525 * r1134528;
        double r1134530 = x;
        double r1134531 = r1134530 * r1134530;
        double r1134532 = 11.0;
        double r1134533 = r1134532 * r1134530;
        double r1134534 = r1134533 * r1134530;
        double r1134535 = r1134534 * r1134526;
        double r1134536 = r1134535 * r1134526;
        double r1134537 = r1134536 - r1134528;
        double r1134538 = 121.0;
        double r1134539 = 4.0;
        double r1134540 = pow(r1134526, r1134539);
        double r1134541 = r1134538 * r1134540;
        double r1134542 = r1134537 - r1134541;
        double r1134543 = 2.0;
        double r1134544 = r1134542 - r1134543;
        double r1134545 = r1134531 * r1134544;
        double r1134546 = r1134529 + r1134545;
        double r1134547 = 5.5;
        double r1134548 = 8.0;
        double r1134549 = pow(r1134526, r1134548);
        double r1134550 = r1134547 * r1134549;
        double r1134551 = r1134546 + r1134550;
        double r1134552 = r1134543 * r1134526;
        double r1134553 = r1134530 / r1134552;
        double r1134554 = r1134551 + r1134553;
        return r1134554;
}
↓
double f(double x, double y) {
        double r1134555 = 0.5;
        double r1134556 = y;
        double r1134557 = x;
        double r1134558 = r1134556 / r1134557;
        double r1134559 = r1134555 / r1134558;
        double r1134560 = r1134557 * r1134557;
        double r1134561 = 2.0;
        double r1134562 = r1134560 * r1134561;
        double r1134563 = r1134559 - r1134562;
        return r1134563;
}

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 58.1

    \[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]

  2. Simplified58.1

    \[\leadsto \color{blue}{\left(\left(x \cdot x\right) \cdot \left(\left(11 \cdot \left(\left(x \cdot y\right) \cdot \left(x \cdot y\right)\right) - {y}^{6}\right) - \left(2 + {y}^{4} \cdot 121\right)\right) + {y}^{6} \cdot 333.75\right) + \left(5.5 \cdot {y}^{8} + \frac{\frac{x}{2}}{y}\right)}\]

  3. Taylor expanded around 0 57.1

    \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y} - 2 \cdot {x}^{2}}\]

  4. Simplified57.1

    \[\leadsto \color{blue}{\frac{0.5}{\frac{y}{x}} - \left(x \cdot x\right) \cdot 2}\]

  5. Final simplification57.1

    \[\leadsto \frac{0.5}{\frac{y}{x}} - \left(x \cdot x\right) \cdot 2\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x y)
  :name "Rump's expression from Stadtherr's award speech"
  :pre (and (== x 77617.0) (== y 33096.0))
  (+ (+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0))) (/ x (* 2.0 y))))